Distributive mixing striation thickness

For measnrement of distributive mixing, striation thickness is a far more practical proposition than measuring surface area (see Chapter 3). In the above example the... 

As mixing progresses, the interfacial area per unit volume increases and the striation thickness decreases. If there is a distribution of striation thickness then not only the mean but also the variance should be taken into consideration for the quality of mixing calculations. In Section 6.3.1 the interfacial area growth, or equivalently the striation thickness reduction, is calculated from geometrical arguments. 

Macromixing The phenomenon whereby residence times of clumps are distributed about a mean value. Mixing on a scale greater than the minimum eddy size or minimum striation thickness, by laminar or turbulent motion. 

Figure 7.27. Twisted-blade type of static mixer operating in the laminar flow regime (a) Distributive mixing mechanism showing, in principle, the reduction in striation thickness produced (f>) Radial mixing contribution...

In Fig. 7.121 reorientation occurs after 100 units of shear strain. Without reorientation the striation thickness reduces to about 10 = after 1000 units of shear strain. With one reorientation the striation thickness reduces to about 10 with two reorientations to about 10, etc. Cleariy, reorientation can achieve improvements in distributive mixing by orders of magnitude, it is a powerful tool in mixing operations. 

In distributive mixing, the flow field produces deformation in the dispersed phase, without inducing breakup. As a consequence, a lamellar morphology of alternating striations of dispersed phase and the matrix is obtained, which can be characterized by the striation thickness distribution. Note that the striation thickness (5) is a function of the initial length scale (la), viscosity of the dispersed phase r]i), total shear strain (y) (product of shear rate and time), volume fraction of the dispersed phase (4>a), and viscosity of the matrix (rim) [59] (Eq. (3.1)) ... 

In the distributive mixing of two similar viscous lamina flow liquids, the degree of mixedness can be assessed by either the total interfacial area between them, or the striation thickness, the two being related ... 

Figure 2.21 Striation thickness versus mixer stage for plasticised PVC with injected striation. Reproduced with permission from G.M. Gale, Distributive Mixing in Plastics Extrusion, Rapra Technology Members Report No.46, Rapra Technology, Shrewsbury, UK, 1980, Figure 7. 1980, Rapra Technology)...

Some methodologies of dynamical systems theory developed from model flows that can be extended to real 3D flows are introduced next. These new tools—stretching calculations, striation thickness distributions, and so on—are essential if one is to obtain detailed statistical information regarding the microstructure emerging in a mixing process and the dynamics of a mixing operation. 

The real power of using stretching computations to characterize chaotic flows lies in the fact that stretching is the link between the macro- and micromixing intensities in laminar mixing flows. In this section we describe the method for computing striation thickness distribution in our 3D example, the Kenics mixer. 

The observed scaling of p has an important physical interpretation Once p approaches the characteristic invariant and statistical distributions generated by the global invariant manifold, it then evolves everywhere at the same rate as the mean density. In other words, if the mean intermaterial area density is doubled, the local density is doubled everywhere. This is important, because it means that the time evolution of time evolution of p at aU locations of the chaotic flow (i.e., intimacy of mixing improves everywhere by the same factor). Similarly, the striation thickness both locally and globally ... 

Another important component of mixing processes, diffusion, remains to be included in the discussion. The ability to measure or predict striation thickness distributions in chaotic flows provides the link between mixing on the macroscopic and microscopic scales. Diffusion and stretching are intimately coupled because as material filaments are stretched by the flow, the rate of diffusion is... 

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